Mathematics – Analysis of PDEs
Scientific paper
2012-02-27
Mathematics
Analysis of PDEs
some explanations were added and some misprints were removed. arXiv admin note: substantial text overlap with arXiv:1011.4236
Scientific paper
By discovering that solutions of the vanishing viscosity approximation (but without flux regularization) to a scalar conservation law with discontinuous flux are equal to a flux crossing point at the interface, we derive entropy conditions which provide well-posedness to a corresponding Cauchy problem. We assume that the flux is such that the maximum principle holds, but we allow multiple flux crossings and we do not need any kind of genuine nonlinearity conditions. Proposed concept is a proper generalization to the standard Kruzhkov entropy conditions and it does not involve transformation of the equation or use of adapted entropies.
Mitrovic Darko
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